Hi all,
I would like to compute the local Peclet number for a highly anysotropic mesh using the following formula.
Let $\mathbf{u} \in \mathbb{R}^2$ be the velocity field. Assume that $\mathbf{u}$ is constant on each element $\tau$ of the mesh.
Let the edges of $\tau$ be $\mathbf{e}_1 = \mathbf{x}_2 - \mathbf{x}_3$, $\mathbf{e}_2 = \mathbf{x}_3 - \mathbf{x}_1$ and $\mathbf{e}_3 = \mathbf{x}_1 - \mathbf{x}_2$, where $\mathbf{x}_i$ are the coordinates of the three vertices of the triangle $\tau$.
Then the local Pe number is defined as
$$ Pe_\tau = \frac{ \max_i\left( \mathbf{u} \cdot \mathbf{e}_i \right) }{2 \nu}, $$
where $\nu$ is the viscosity.
Is there an UFL expression to easily evaluate the edges $\mathbf{e}_i$ of $\tau$?
Thanks a lot,
Umberto
